代写ECO204程序、代写C++，Java编程

日期：2023-03-02 11:20

ECO204 2022-2023

A STEP-BY-STEP GUIDE TO PROJECT 2(04)

Project 2(04): Construct a one-month-holding-period financial portfolio in February 2023 with:

Fraction 1 of funds invested in a “Risk-Free Asset”

Fraction of funds (with ≥ 0) invested in a “Synthetic

Risky Asset” (SRA) which consists of four risky assets with

investment weights 1, . . , 4 ( ? 0 and σ = 1)

1 in “Equity #1” 2 in “Equity #2”

3 in “Equity #3”

OR “Oil”

4 in a

“Corporate-

Bond”

You are the CIO at a “family-fund”.

This morning (“today” = Jan 31st 2023), the (risk-averse) Board of Directors (Ivey &

Queens graduates) put you in-charge of Project 2(04):

Project 2(04) harkens back to time you took ECO204 and aced the “Shred Ivey-

Queens Project” by constructing a financial portfolio by four different methods.

You’re going to prove your mettle – and once again shred those Queens & Ivey

snobs – by constructing four different models of the Project 2(04) financial portfolio. 2

Project 2(04): “Synopsis”

Ajaz Hussain, Economics, University of Toronto (STG)

ECO204 2022-2023

Lecture & Tutorial Portfolios: Quick Review

4Agent invests $ of her own funds in a financial portfolio consisting of:

Fraction (1 ? ) invested in a Risk Free Asset Fraction invested in ONE actual risky asset

A “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:

Fraction 1 of “SRA” in a

real Risky Asset 1

Fraction 2 of “SRA” in a

real Risky Asset 2

Fraction 3 of “SRA” in a

real Asset 3

Agent invests $ of her own funds in a financial portfolio consisting of:

Fraction (1 ? ) invested in a Risk

Free Asset

Fraction invested in a “SRA”

consisting of ≥ 1 actual risky

assets:

Fraction 1 of

“SRA” in Risky

Asset 1

Fraction 2 of

“SRA” in Risky

Asset 2

Fraction 3 of

“SRA” in Risky

Asset 3

Portfolio “A”

Portfolio “B”

Portfolio “C”

Portfolio A

Portfolio B

Portfolio C

Use Portfolio A algebra by

treating SRA as “the” risky asset

Recall: The “Algebra” of Constructing Portfolio of a Risk Free and Synthetic Risky Asset

For the sake of illustration,

suppose the SRA consists

of 3 risky assets

Calculate optimal investment weights of risky assets in

SRA by maximizing the SRA’s Sharpe Ratio

Calculate optimal fraction invested in “risk free asset”

and “SRA as the risky asset” (with return-risk and

) by maximizing Mean-Variance Utility.

In practice, you’d need the value of parameter [see W12

Lecture, W14 Tutorial]

Result

“Optimal Portfolio” of a Risk-Free-Asset and a SRA

consisting of ≥ 1 risky assets

5

A “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:

Fraction 1 of “SRA” in a

real Risky Asset 1

Fraction 2 of “SRA” in a

real Risky Asset 2

Fraction 3 of “SRA” in a

real Asset 3

Agent invests $ of her own funds in a financial portfolio consisting of:

Fraction (1 ? ) invested in a Risk

Free Asset

Fraction invested in a “SRA”

consisting of ≥ 1 actual risky

assets:

Fraction 1 of

“SRA” in Risky

Asset 1

Fraction 2 of

“SRA” in Risky

Asset 2

Fraction 3 of

“SRA” in Risky

Asset 3

Agent invests $ of her own funds in a financial portfolio consisting of:

Fraction (1 ? ) invested in a Risk Free Asset Fraction invested in SRA

Recall: The “Mechanics” of Constructing Portfolio of Risk Free and Synthetic Risky Asset

Ajaz Hussain, Economics, University of Toronto (STG)

ECO204 2022-2023

“Minimal Data” Required to Construct Portfolio

of a Risk Free and a Synthetic Risky Asset

7“Minimal Data” for Constructing Portfolio with a Risk Free and a Synthetic Risky Asset

A “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:

Fraction 1 of “SRA” in a

real Risky Asset 1

Fraction 2 of “SRA” in a

real Risky Asset 2

Fraction 3 of “SRA” in a

real Asset 3

Agent invests $ of her own funds in a financial portfolio consisting of:

Fraction (1 ? ) invested in a Risk Free Asset Fraction invested in SRA

max

1,2,3

Sharpe Ratio of SRA =

Risk Premium of SRA

Risk of SRA

“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)

for = , . . , for , = , . . ,

“You”

Risk Free:

FRED Series

DGS3MO

Randomly

assigned

“Equity #1”

from CRSP

Randomly

assigned

“Equity #2”

from CRSP

Randomly

assigned

“Equity #3”

from CRSP

Randomly

assigned a

Corporate

Bond from a

Blackrock ETF

“Commodity”:

Oil FRED

Series

DCOILWTICO

8

Project 2(04) Assets & “Project 2-Excel-Template”

Project 2(04): Construct a one-month-holding-period financial portfolio in February 2023 with:

Fraction 1 ? of funds invested in

a “Risk-Free Asset”

Fraction of funds (with ≥ 0) invested in a “Synthetic Risky

Asset” (SRA) consisting of four risky assets with investment

weights , = 1, . . , 4

1 in

“Equity #1”

2 in

“Equity #2”

3 in

“Equity #3”

OR “Oil”

4 in a

“Corporate-

Bond”

Project 2(04) Excel-Template-Demo-Portfolio: Construct a one-month-holding-period financial portfolio in February 2023 with:

Fraction 1 ? of funds invested in

a “Risk-Free Asset” FRED Series DGS3MO

Fraction of funds (with ≥ 0) invested in a “Synthetic Risky Asset” (SRA)

consisting of five risky assets with investment weights , = 1, . . , 5

1 in Equity #1:

APTV

2 in “Equity

#2”: CCL

3 in “Equity

#3”: MTN

4 in a “Equity

#4”: EXAS

5 in a

“Corporate-

Bond”: SPRINT

To help you, I’ve posted an “Excel-Template” for the following “DEMO” portfolio ?

9“Asset” Comment

“Risk Free Asset”

FRED Series DGS3MO

Download monthly data via FRED Excel Add-in or FRED website. See FRED-DGS3MO tab and W14 Tutorial on how to

transform FRED data to obtain monthly (by “compounded method”) in Feb 2023.

By definition: = 0, = 0 for all = 1, . . .

CRSP “Equities”

See Equity-Bond-Assign tab for CRSP equities assigned to you and download data from CRSP.

Currently, CRSP reports “returns” through June 2022. See Lecture Delivered W11 on “cleaning” and “pruning” CRSP

data for a common “date range” (see Equities-CRSP-Jun22 tab for demo example).

For July 2022 – Jan 2023 “data”, use Google Sheets in Equities-Google-Jan23 tab to download “daily prices”

[Urge you to look at the Excel “setup” and “formulas”]

Combine CRSP and Google equities data sets (see Equities-Data tab).

S&P500

For reasons to be explained later, we will need data on SP500 returns.

Best option is to download SP500 Nominal Index from multpl.com and compute returns for the date range of the “final

equities” data set (See Lecture Delivered W11 and SP500 tab)

“Corporate-Bond”

Download the Blackrock-IBHC-ETF file (updated daily) from here? “clean/format” the data (see Blackrock-IBHC-

ETF tab) ? Extract the row corresponding to your bond ? copy & paste & transpose that row in new worksheet

(see DEMO-Sprint tab)

Use the bond’s ISIN # to find “today’s price” (be creative and put some elbow grease).

Use “Solver” to compute a “finely-tuned” YTM monthly rate (see Table in Columns H-L in DEMO-Sprint tab).

Research your corporate-bond rating (AAA, AA, A, B, BB, BBB, CCC) ? Go to Corp-Bonds-Quandl tab and take

note of data-series (monthly yields) corresponding to your bond rating

“Commodity -- Oil”:

FRED Series

DCOILWTICO

NOT in Excel-Template. Download monthly data of Oil prices ($/barrel) via FRED Excel Add-in or FRED website ?

Forecast next month’s Oil price by assuming growth rate of Oil prices is Normally distributed and “picking” a growth

rate at random from this distribution (see Gold Claims Case)

Combine the final equities returns data set, SP500 returns data set, Quandl-Bond monthly yield data series corresponding to your bond’s rating,

and the Oil returns data set, over the date range of the “final equities” data set to obtain a “unified” data set (see ALL-DATA tab).

“Minimal Data” for Constructing Portfolio with a Risk Free and a Synthetic Risky Asset

10

“Minimal Data” for Constructing Portfolio with a Risk Free and a Synthetic

Risky Asset

(Shown for illustrative purposes) The “unified data set of monthly returns” (see ALL-DATA tab)

“Month” Equity 1 monthly returns Equity 2 monthly returns Equity 3 monthly returns SP500 monthly returns Oil Price monthly returns

Monthly Yields on Quandl-

bond with same rating as

your corporate bond

Month-1 # # # # # #

…

Month-N # # # # # #

See ALL-DATA tab.

Ajaz Hussain, Economics, University of Toronto (STG)

ECO204 2022-2023

Four Methods for “Estimating” the “Data Required to

Construct Portfolio of a Risk Free Asset and a Synthetic

Risky Asset (with = , . . , Risky Assets)

Four Methods for “Estimating” the “Data Required to Construct Portfolio of a Risk Free

Asset and a Synthetic Risky Asset (with = , . . , Risky Assets)

Stats Stats-Shrinkage

Monte-Carlo

Simulations Wiener

Process

Monte-Carlo

Simulations Ito

Process

Calculate fraction of funds allocated to SRA

Four Methods for “Estimating” the “Data Required to Construct Portfolio of a Risk Free

Asset and a Synthetic Risky Asset”

13

Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Stats Approach”

“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)

Asset Expected Return: Future Risk: Future Covariance

Risk Free Asset 0 , = 0

Equities ,?

Corporate-Bond (Monthly) YTM of Quandl Bond with the

same rating

Where +1 estimated

by technique used in “Gold

Claims” case

oil ,?

See Portfolio-Stats tab.

Note: Using “baseline ” value such that 100% invested in SRA

14

Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Stats-Shrinkage Approach”

“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)

Asset Expected Return: Future Risk: Future Covariance

Risk Free Asset 0 , = 0

Equities + 500

Corporate-Bond (Monthly) YTM of Quandl Bond with the

same rating

Where +1 estimated

by technique used in “Gold

Claims” case

oil ,?

See Portfolio-Stats-Shrinkage tab.

Note: Using “baseline ” value such that 100% invested in SRA

15

Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Monte-Carlo Simulations Wiener

Process” Approach”

“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)

Asset Expected Return: Future Risk: Future Covariance

Risk Free Asset 0 , = 0

Equities of the simulations of the simulations ,?

Using equity simulations

Corporate-Bond (Monthly) YTM of Quandl Bond with the same

rating

,?

Using equity simulations

Oil Prices +1 ?

Where +1 estimated by

technique used in “Gold Claims”

case

oil ,?

Using equity simulations

Assume equity ~ ,

2

Simulate (say) 1,000 rounds of

Randomly select simulations

See RET-Wiener-Process tab and Portfolio-Wiener-Process tab.

Note: Using “baseline ” value such that 100% invested in SRA

16

Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Monte-Carlo Simulations Wiener

Process” Approach”

“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)

Asset Expected Return: Future Risk: Future Covariance

Risk Free Asset 0 , = 0

Equities of the simulations of the simulations ,?

Using equity simulations

Corporate-Bond (Monthly) YTM of Quandl Bond with the same

rating

Using equity simulations

Oil Prices +1

Where +1 estimated by

technique used in “Gold Claims”

case

oil ,

Using equity simulations

Assume equity ~

2

2

, 2

Simulate (say) 1,000 rounds of

Randomly select simulations

See RET-Ito-Process tab and Portfolio-Ito-Process tab.

Note: Using “baseline ” value such that 100% invested in SRA